Conventionally, with improvements in computer performance and advances in electromagnetic field analysis methods, the simulation of electrical devices such as motors and generators that use magnetic materials has become widely performed in a variety of settings. Difference methods and finite element methods are typically used as a method of electromagnetic field analysis. Recently, significant emphasis has been placed on the efficiency of electrical devices as a means of reducing CO2 and preventing global warming. Accordingly, there are greater expectations concerning simulation.
With respect to magnetic metal materials used in electrical devices, for example, in the case of magnetic steel sheeting, loss within the magnetic substrate is classified as hysteresis loss (which is a cause of hysteresis in the magnetic substrate), classic eddy current loss from eddy currents occurring at the magnetic substrate, and anomalous eddy current loss. In the case of magnetic materials used in devices driven at high frequencies, e.g., high-resistivity magnetic materials such as ferrite and amorphous powder material, loss within the magnetic material is classified as hysteresis loss and residual loss (i.e., dynamic magnetic loss).
High-resistivity magnetic materials include oxide magnetic materials of which ferrite is a typical example, amorphous powder materials formed of pressure molded magnetic metal powders processed for electrical insulation, magnetic compound materials of a magnetic metal material and an oxide or nitride, etc.
To calculate the efficiency of an electrical device, the loss within the magnetic substrate has to be accurately obtained. Recently, higher frequencies are applied to the magnetic materials used in motors, etc. consequent to advances in driving technology of which inverters are a typical example and electrical devices are driven on conditions that include, for example, harmonic components on the order of kHz.
One method is used by a finite element method as a method of calculating loss (see, for example, Yamazaki, K., et al, “Iron Loss Analysis of IPM Motor Considering Carrier Harmonics”, IEEJ Trans. IA, Vol. 125, No. 7, 2005). Hysterisis loss Wh and eddy current loss We when a high frequency magnetic field is applied to a magnetic substrate model are respectively calculated by analysis formulae (1) and (2).
                              W          h                =                              ∑            n                    ⁢                                          ⁢                      {                                          ∫                iron                            ⁢                                                K                  h                                ⁢                                                      D                    ⁡                                          (                      nf                      )                                                        2                                ⁢                                  (                                                            B                                              r                        ,                        n                                            2                                        +                                          B                                              θ                        ,                        n                                            2                                                        )                                ⁢                                                                  ⁢                                  ⅆ                  v                                                      }                                              (        1        )                                          W          e                =                              ∑            n                    ⁢                                          ⁢                      {                                          ∫                iron                            ⁢                                                K                  e                                ⁢                                                      D                    ⁡                                          (                      nf                      )                                                        2                                ⁢                                  (                                                            B                                              r                        ,                        n                                            2                                        +                                          B                                              θ                        ,                        n                                            2                                                        )                                ⁢                                                                  ⁢                                  ⅆ                  v                                                      }                                              (        2        )            
Where, Kh is a hysterisis loss coefficient determined by the magnetic material; Ke is an eddy current loss coefficient determined by the magnetic material; f represents frequency; D represents the density of the magnetic substrate; Br,n and Bθ,n respectively represent radial direction and rotational direction magnetic flux densities. In this method, the values differ from the values under actual operating conditions of the electrical device and accurate hysterisis loss and anomalous eddy current loss is difficult to calculate.
Although Matsuo, T., et al, in “Representation of minor hysteresis loops of a silicon steel sheet using stop and play models”, http://www.sciencedirect.com, Physica B, Volume 372, Issues 1-2, 1 Feb. 2006, pages 25-29 considers calculation of a hysterisis curve for a magnetic substrate by an analysis method called “Stop and Play Models”, such calculation has yet to be used in actual analysis.
As a simulation method that deals with the magnetic domain structure and domain walls of a magnetic substrate, the calculation method by micromagnetics recited by William Fuller Brown, Jr. in “Thermal Fluctuations of a Single-Domain Particle”, Physical Review, Volume 130, Number 5, 1 Jun. 1963 is known. Matsuo, T., et al in “A Study of Demagnetizing Field in Micromagnetic Simulation under Periodic Boundary Condition”, The Institute of Electrical Engineers of Japan, MAG-10-17, SA10-17, RM10-17, January 2010 consider a hysterisis curve by micromagnetics. However, the method is not applied in actual analysis.
In high frequency transducers and high frequency inductors that use high-resistivity magnetic material, loss consequent to the dynamic magnetization process including resonance phenomena and ferromagnetic resonance of domain walls occurs. Although driving on the order of MHz is considered for these devices and for reducing device size/improving efficiency, in order to do this, design that takes into consideration the resonance and ferromagnetic resonance of domain walls is necessary.
FIG. 15 is a graph of actual data indicating the frequency dependency of permeability when magnetic resonance is present (see, for example, Kawano, K, et al, “The grain size effect on the magnetic properties in NiZn ferrite and the quality factor of the inductor”). The imaginary portion μ” of permeability indicates the phase difference of a magnetic field H and a magnetic flux density B, where the greater the imaginary portion μ” is the greater loss is.
Current is difficult to pass through magnetic substrates of a high-resistivity magnetic material, such as ferrite and an amorphous powder material. Meanwhile, according to higher drive frequencies consequent to magnetic resonance such as resonance and ferromagnetic resonance of the domain walls, the loss within the magnetic substrate tends to increase. Therefore, accurate estimation of the loss within the magnetic substrate is an important matter in terms of optimizing the structure and materials of devices. However, with the technologies above, calculation that takes into consideration physical phenomena like magnetic resonance phenomena (such as resonance and ferromagnetic resonance of domain walls) and eddy currents occurring in high-resistivity magnetic material cannot be handled.